OpenRaiser/Intern-Atlas huggingface dataset:
Stable and robust sampling strategies for compressive imaging
Venue: arXiv cs.CV 2013
Year: 2013

In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence suggests that superior image reconstruction can be obtained through variable density sampling strategies that concentrate on lower frequencies. The wavelet and Fourier transform domains are not incoherent because low-order wavelets and low-order frequencies are correlated, so compressive sensing theory does not immediately imply sampling strategies and reconstruction guarantees. In this paper we turn to a more refined notion of coherence -- the so-called local coherence -- measuring for each sensing vector separately how correlated it is to the sparsity basis. For Fourier measurements and Haar wavelet sparsity, the local coherence can be controlled and bounded explicitly, so for matrices comprised of frequencies sampled from a suitable inverse square power-law density, we can prove the restricted isometry property with near-optimal embedding dimensions. Consequently, the variable-density sampling strategy we provide allows for image reconstructions that are stable to sparsity defects and robust to measurement noise. Our results cover both reconstruction by $\ell_1$-minimization and by total variation minimization. The local coherence framework developed in this paper should be of independent interest in sparse recovery problems more generally, as it implies that for optimal sparse recovery results, it suffices to have bounded \emph{average} coherence from sensing basis to sparsity basis -- as opposed to bounded maximal coherence -- as long as the sampling strategy is adapted accordingly.
Heuristic algorithms for the bipartite unconstrained 0-1 quadratic programming problem
Venue: arXiv cs.DM 2013
Year: 2013

We study the Bipartite Unconstrained 0-1 Quadratic Programming Problem (BQP) which is a relaxation of the Unconstrained 0-1 Quadratic Programming Problem (QP). Applications of the BQP include mining discrete patterns from binary data, approximating matrices by rank-one binary matrices, computing cut-norm of a matrix, and solving optimization problems such as maximum weight biclique, bipartite maximum weight cut, maximum weight induced subgraph of a bipartite graph, etc. We propose several classes of heuristic approaches to solve the BQP and discuss a number of construction algorithms, local search algorithms and their combinations. Results of extensive computational experiments are reported to establish the practical performance of our algorithms. For this purpose, we propose several sets of test instances based on various applications of the BQP. Our algorithms are compared with state-of-the-art heuristics for QP which can also be used to solve BQP with reformulation. We also study theoretical properties of the neighborhoods and algorithms. In particular, we establish complexity of all neighborhood search algorithms and establish tight worst-case performance ratio for the greedy algorithm.
A new Truncated Fourier Transform algorithm
Venue: arXiv cs.SC 2013
Year: 2013

Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in terms of ring operations, is comparable to existing not-in-place TFT methods. We also describe a transformation that maps between two families of TFT algorithms that use different sets of evaluation points.
Realizability algebras III: some examples
Venue: arXiv cs.LO 2013
Year: 2013

We use the technique of "classical realizability" to build new models of ZF + DC in which R is not well ordered. This gives new relative consistency results, probably not obtainable by forcing. This gives also a new method to get programs from proofs of arithmetical formulas with dependent choice.
A Scalable Null Model for Directed Graphs Matching All Degree Distributions: In, Out, and Reciprocal
Venue: arXiv cs.SI 2013
Year: 2013

Degree distributions are arguably the most important property of real world networks. The classic edge configuration model or Chung-Lu model can generate an undirected graph with any desired degree distribution. This serves as a good null model to compare algorithms or perform experimental studies. Furthermore, there are scalable algorithms that implement these models and they are invaluable in the study of graphs. However, networks in the real-world are often directed, and have a significant proportion of reciprocal edges. A stronger relation exists between two nodes when they each point to one another (reciprocal edge) as compared to when only one points to the other (one-way edge). Despite their importance, reciprocal edges have been disregarded by most directed graph models. We propose a null model for directed graphs inspired by the Chung-Lu model that matches the in-, out-, and reciprocal-degree distributions of the real graphs. Our algorithm is scalable and requires $O(m)$ random numbers to generate a graph with $m$ edges. We perform a series of experiments on real datasets and compare with existing graph models.
The performance of orthogonal multi-matching pursuit under RIP
Venue: arXiv cs.IT 2013
Year: 2013

The orthogonal multi-matching pursuit (OMMP) is a natural extension of orthogonal matching pursuit (OMP). We denote the OMMP with the parameter $M$ as OMMP(M) where $M\geq 1$ is an integer. The main difference between OMP and OMMP(M) is that OMMP(M) selects $M$ atoms per iteration, while OMP only adds one atom to the optimal atom set. In this paper, we study the performance of orthogonal multi-matching pursuit (OMMP) under RIP. In particular, we show that, when the measurement matrix A satisfies $(9s, 1/10)$-RIP, there exists an absolutely constant $M_0\leq 8$ so that OMMP(M_0) can recover $s$-sparse signal within $s$ iterations. We furthermore prove that, for slowly-decaying $s$-sparse signal, OMMP(M) can recover s-sparse signal within $O(\frac{s}{M})$ iterations for a large class of $M$. In particular, for $M=s^a$ with $a\in [0,1/2]$, OMMP(M) can recover slowly-decaying $s$-sparse signal within $O(s^{1-a})$ iterations. The result implies that OMMP can reduce the computational complexity heavily.
Symmetric Determinantal Representations in Characteristic 2
Venue: arXiv cs.CC 2013
Year: 2013

This paper studies Symmetric Determinantal Representations (SDR) in characteristic 2, that is the representation of a multivariate polynomial P by a symmetric matrix M such that P=det(M), and where each entry of M is either a constant or a variable. We first give some sufficient conditions for a polynomial to have an SDR. We then give a non-trivial necessary condition, which implies that some polynomials have no SDR, answering a question of Grenet et al. A large part of the paper is then devoted to the case of multilinear polynomials. We prove that the existence of an SDR for a multilinear polynomial is equivalent to the existence of a factorization of the polynomial in certain quotient rings. We develop some algorithms to test the factorizability in these rings and use them to find SDRs when they exist. Altogether, this gives us polynomial-time algorithms to factorize the polynomials in the quotient rings and to build SDRs. We conclude by describing the case of Alternating Determinantal Representations in any characteristic.
Brandt's Fully Private Auction Protocol Revisited
Venue: arXiv cs.CR 2013
Year: 2013

Auctions have a long history, having been recorded as early as 500 B.C. Nowadays, electronic auctions have been a great success and are increasingly used. Many cryptographic protocols have been proposed to address the various security requirements of these electronic transactions, in particular to ensure privacy. Brandt developed a protocol that computes the winner using homomorphic operations on a distributed ElGamal encryption of the bids. He claimed that it ensures full privacy of the bidders, i.e. no information apart from the winner and the winning price is leaked. We first show that this protocol -- when using malleable interactive zero-knowledge proofs -- is vulnerable to attacks by dishonest bidders. Such bidders can manipulate the publicly available data in a way that allows the seller to deduce all participants' bids. Additionally we discuss some issues with verifiability as well as attacks on non-repudiation, fairness and the privacy of individual bidders exploiting authentication problems.
Tree t-spanners in Outerplanar Graphs via Supply Demand Partition
Venue: arXiv cs.DS 2013
Year: 2013

A tree t-spanner of an unweighted graph G is a spanning tree T such that for every two vertices their distance in T is at most t times their distance in G. Given an unweighted graph G and a positive integer t as input, the tree t-spanner problem is to compute a tree t-spanner of G if one exists. This decision problem is known to be NP-complete even in the restricted class of unweighted planar graphs. We present a linear-time reduction from tree t-spanner in outerplanar graphs to the supply-demand tree partition problem. Based on this reduction, we obtain a linear-time algorithm to solve tree t-spanner in outerplanar graphs. Consequently, we show that the minimum value of t for which an input outerplanar graph on n vertices has a tree t-spanner can be found in O(n log n) time.
Dominator Tree Certification and Independent Spanning Trees
Venue: arXiv cs.DS 2013
Year: 2013

How does one verify that the output of a complicated program is correct? One can formally prove that the program is correct, but this may be beyond the power of existing methods. Alternatively one can check that the output produced for a particular input satisfies the desired input-output relation, by running a checker on the input-output pair. Then one only needs to prove the correctness of the checker. But for some problems even such a checker may be too complicated to formally verify. There is a third alternative: augment the original program to produce not only an output but also a correctness certificate, with the property that a very simple program (whose correctness is easy to prove) can use the certificate to verify that the input-output pair satisfies the desired input-output relation. We consider the following important instance of this general question: How does one verify that the dominator tree of a flow graph is correct? Existing fast algorithms for finding dominators are complicated, and even verifying the correctness of a dominator tree in the absence of additional information seems complicated. We define a correctness certificate for a dominator tree, show how to use it to easily verify the correctness of the tree, and show how to augment fast dominator-finding algorithms so that they produce a correctness certificate. We also relate the dominator certificate problem to the problem of finding independent spanning trees in a flow graph, and we develop algorithms to find such trees. All our algorithms run in linear time. Previous algorithms apply just to the special case of only trivial dominators, and they take at least quadratic time.
Explicit Lower Bounds via Geometric Complexity Theory
Venue: arXiv cs.CC 2013
Year: 2013

We prove the lower bound R(M_m) \geq 3/2 m^2 - 2 on the border rank of m x m matrix multiplication by exhibiting explicit representation theoretic (occurence) obstructions in the sense of the geometric complexity theory (GCT) program. While this bound is weaker than the one recently obtained by Landsberg and Ottaviani, these are the first significant lower bounds obtained within the GCT program. Behind the proof is the new combinatorial concept of obstruction designs, which encode highest weight vectors in Sym^d\otimes^3(C^n)^* and provide new insights into Kronecker coefficients.
Linear-Nonlinear-Poisson Neuron Networks Perform Bayesian Inference On Boltzmann Machines
Venue: arXiv cs.AI 2013
Year: 2013

One conjecture in both deep learning and classical connectionist viewpoint is that the biological brain implements certain kinds of deep networks as its back-end. However, to our knowledge, a detailed correspondence has not yet been set up, which is important if we want to bridge between neuroscience and machine learning. Recent researches emphasized the biological plausibility of Linear-Nonlinear-Poisson (LNP) neuron model. We show that with neurally plausible settings, the whole network is capable of representing any Boltzmann machine and performing a semi-stochastic Bayesian inference algorithm lying between Gibbs sampling and variational inference.
The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
Venue: arXiv cs.DM 2013
Year: 2013

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogues to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting, and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.
Matrix approach to rough sets through vector matroids over a field
Venue: arXiv cs.AI 2013
Year: 2013

Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in optimization. Therefore, it is necessary to connect matroids with rough sets. In this paper, we take field into consideration and introduce matrix to study rough sets through vector matroids. First, a matrix representation of an equivalence relation is proposed, and then a matroidal structure of rough sets over a field is presented by the matrix. Second, the properties of the matroidal structure including circuits, bases and so on are studied through two special matrix solution spaces, especially null space. Third, over a binary field, we construct an equivalence relation from matrix null space, and establish an algebra isomorphism from the collection of equivalence relations to the collection of sets, which any member is a family of the minimal non-empty sets that are supports of members of null space of a binary dependence matrix. In a word, matrix provides a new viewpoint to study rough sets.
Sub-Nyquist Radar via Doppler Focusing
Venue: arXiv cs.IT 2013
Year: 2013

We investigate the problem of a monostatic pulse-Doppler radar transceiver trying to detect targets, sparsely populated in the radar's unambiguous time-frequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem, but either do not address sample rate reduction, impose constraints on the radar transmitter, propose CS recovery methods with prohibitive dictionary size, or perform poorly in noisy conditions. Here we describe a sub-Nyquist sampling and recovery approach called Doppler focusing which addresses all of these problems: it performs low rate sampling and digital processing, imposes no restrictions on the transmitter, and uses a CS dictionary with size which does not increase with increasing number of pulses P. Furthermore, in the presence of noise, Doppler focusing enjoys an SNR increase which scales linearly with P, obtaining good detection performance even at SNRs as low as -25dB. The recovery is based on the Xampling framework, which allows reducing the number of samples needed to accurately represent the signal, directly in the analog-to-digital conversion process. After sampling, the entire digital recovery process is performed on the low rate samples without having to return to the Nyquist rate. Finally, our approach can be implemented in hardware using a previously suggested Xampling prototype.
Optimal Information-Theoretic Wireless Location Verification
Venue: arXiv cs.IT 2013
Year: 2013

We develop a new Location Verification System (LVS) focussed on network-based Intelligent Transport Systems and vehicular ad hoc networks. The algorithm we develop is based on an information-theoretic framework which uses the received signal strength (RSS) from a network of base-stations and the claimed position. Based on this information we derive the optimal decision regarding the verification of the user's location. Our algorithm is optimal in the sense of maximizing the mutual information between its input and output data. Our approach is based on the practical scenario in which a non-colluding malicious user some distance from a highway optimally boosts his transmit power in an attempt to fool the LVS that he is on the highway. We develop a practical threat model for this attack scenario, and investigate in detail the performance of the LVS in terms of its input/output mutual information. We show how our LVS decision rule can be implemented straightforwardly with a performance that delivers near-optimality under realistic threat conditions, with information-theoretic optimality approached as the malicious user moves further from the highway. The practical advantages our new information-theoretic scheme delivers relative to more traditional Bayesian verification frameworks are discussed.
A Rewriting View of Simple Typing
Venue: arXiv cs.PL 2013
Year: 2013

This paper shows how a recently developed view of typing as small-step abstract reduction, due to Kuan, MacQueen, and Findler, can be used to recast the development of simple type theory from a rewriting perspective. We show how standard meta-theoretic results can be proved in a completely new way, using the rewriting view of simple typing. These meta-theoretic results include standard type preservation and progress properties for simply typed lambda calculus, as well as generalized versions where typing is taken to include both abstract and concrete reduction. We show how automated analysis tools developed in the term-rewriting community can be used to help automate the proofs for this meta-theory. Finally, we show how to adapt a standard proof of normalization of simply typed lambda calculus, for the rewriting approach to typing.
Interactive Interference Alignment
Venue: arXiv cs.IT 2013
Year: 2013

We study interference channels (IFC) where interaction among sources and destinations is enabled, e.g., both sources and destinations can talk to each other using full-duplex radios. The interaction can come in two ways: 1) {\em In-band interaction:} sources and destinations can transmit and listen in the same channel simultaneously, enabling interaction. 2) {\em out-of-band interaction:} destinations talk back to the sources on an out-of-band channel, possible from white-space channels. The flexibility afforded by interaction among sources and destinations allows for the derivation of interference alignment (IA) strategies that have desirable "engineering properties": insensitivity to the rationality or irrationality of channel parameters, small block lengths and finite SNR operations. We show that for several classes of interference channels the interactive interference alignment scheme can achieve the optimal degrees of freedom. In particular, we show the {\em first simple scheme} (having finite block length, for channels having no diversity) for $K=3,4$ that can achieve the optimal degrees of freedom of $\frac{K}{2}$ even after accounting for the cost of interaction. We also give simulation results on the finite SNR performance of interactive alignment under some settings. On the technical side, we show using a Gröbner basis argument that in a general network potentially utilizing cooperation and feedback, the optimal degrees of freedom under linear schemes of a fixed block length is the same for channel coefficients with probability 1. Furthermore, a numerical method to estimate this value is also presented. These tools have potentially wider utility in studying other wireless networks as well.
Data Mining Based Technique for IDS Alerts Classification
Venue: arXiv cs.CR 2013
Year: 2013

Intrusion detection systems (IDSs) have become a widely used measure for security systems. The main problem for those systems results is the irrelevant alerts on those results. We will propose a data mining based method for classification to distinguish serious alerts and irrelevant one with a performance of 99.9% which is better in comparison with the other recent data mining methods that have reached the performance of 97%. A ranked alerts list also created according to alerts importance to minimize human interventions.
Blind Signal Separation in the Presence of Gaussian Noise
Venue: arXiv cs.LG 2013
Year: 2013

A prototypical blind signal separation problem is the so-called cocktail party problem, with n people talking simultaneously and n different microphones within a room. The goal is to recover each speech signal from the microphone inputs. Mathematically this can be modeled by assuming that we are given samples from an n-dimensional random variable X=AS, where S is a vector whose coordinates are independent random variables corresponding to each speaker. The objective is to recover the matrix A^{-1} given random samples from X. A range of techniques collectively known as Independent Component Analysis (ICA) have been proposed to address this problem in the signal processing and machine learning literature. Many of these techniques are based on using the kurtosis or other cumulants to recover the components. In this paper we propose a new algorithm for solving the blind signal separation problem in the presence of additive Gaussian noise, when we are given samples from X=AS+η, where ηis drawn from an unknown, not necessarily spherical n-dimensional Gaussian distribution. Our approach is based on a method for decorrelating a sample with additive Gaussian noise under the assumption that the underlying distribution is a linear transformation of a distribution with independent components. Our decorrelation routine is based on the properties of cumulant tensors and can be combined with any standard cumulant-based method for ICA to get an algorithm that is provably robust in the presence of Gaussian noise. We derive polynomial bounds for the sample complexity and error propagation of our method.
Fourier-Bessel rotational invariant eigenimages
Venue: arXiv cs.CV 2013
Year: 2013

We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two dimensional images, and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier-Bessel basis for the disk. Because the images are bandlimited in the Fourier domain, we use a sampling criterion to truncate the Fourier-Bessel expansion such that the maximum amount of information is preserved without the effect of aliasing. The constructed covariance matrix is invariant to rotation and reflection and has a special block diagonal structure. PCA is efficiently done for each block separately. This Fourier-Bessel based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.